Method for constructing linear luenberger observer for vehicle control

ABSTRACT

The present invention discloses a method for constructing linear luenberger observer for vehicle control. The method for constructing linear luenberger observer for vehicle control comprises the following steps: step 1: building a state-space equation of a driving system of a vehicle to judge observability of the driving system; step 2: dividing the state of the driving system into blocks, and reconstructing state components of the driving system to obtain an rewritten state observation equation of the driving system; step 3: introducing transformation into the rewritten state equation of the driving system to obtain an expression equation and an error equation of the Luenberger observer. The linear luenberger observer constructed by the present invention has low implementation difficulty. High-frequency noise in an output signal of a rotational speed sensor is reduced.

TECHNICAL FIELD

The present invention belongs to the field of vehicle controltechnologies, and in particular relates to a method for constructinglinear Luenberger observer for vehicle control.

BACKGROUND OF THE INVENTION

In view of the cost, the safety and mounting conditions, the existingproduct-level vehicle is rarely mounted with a torque sensor to directlymeasure the torque of a drive shaft, but indirectly acquires it throughthe existing measurable information. Compared with the torque sensor, arotational speed sensor has low cost. The rotational speed sensor suchas a photoelectric coder can be used for monitoring the rotational speedof each element of a power transmission system.

However, the existing method for measuring the torque of the drive shaftis influenced by a rotational speed sensor of a vehicle wheel and anelectric motor B rotary transformer error. When an integral method isused for measuring the torque of the drive shaft, sensor signal noises,outside interference and the like may cause accumulation to anestimation result under the action of an integral. Therefore, a largeerror is generated between an estimation value and an actual value.Especially, when there is an error between an estimation initial valueand an actual initial value, an estimation error is increased, so theapplication difficulty is large in practice.

SUMMARY OF THE INVENTION

An objective of the present invention is to provide a method forconstructing linear Luenberger observer for vehicle control, which feedsback by utilizing actual measurable information and corrects anestimation result in real time such that an estimation value can greatlytrack an actual value and can resist outside interference to reduce anerror between the estimation value and the actual value; at this time,the method is suitable for practical application.

The present invention adopts the following technical solution: a methodfor constructing linear Luenberger observer for vehicle controlspecifically comprises the following steps:

step 1: building a state-space equation of a driving system of a vehicleto judge observability of the driving system;

wherein a state equation of the driving system is built by utilizing{dot over (θ)}_(B), {dot over (θ)}_(v) and T_(s) as state variables,{dot over (θ)}_(B) and {dot over (θ)}_(v) as the output of the drivingsystem, and T_(P) and T_(v) as the input of the driving system; thestate-space equation of the driving system is shown in equation (1):

$\begin{matrix}\left\{ \begin{matrix}{\hat{x} = {{Ax} + {Bu}}} \\{y = {Cx}}\end{matrix} \right. & (1)\end{matrix}$

wherein x is the input of the state-space equation; y is the output ofthe state-space equation;

$\mspace{20mu} {{x = \begin{bmatrix}\theta_{1} \\\text{?} \\\text{?}\end{bmatrix}},{A = \begin{bmatrix}{- \frac{\text{?}}{J_{P}}} & 0 & {- \frac{1}{J_{p}i_{v}}} \\0 & {- \frac{C_{v}}{J_{v}}} & \frac{1}{J_{v}} \\{\frac{\text{?}}{\text{?}} - \frac{\text{?}}{\text{?}}} & {\frac{C_{s}C_{v}}{J_{v}} - \text{?}} & {{- \frac{\text{?}}{J_{p}i_{r}^{2}}} - \frac{\text{?}}{J_{v}}}\end{bmatrix}},\mspace{20mu} {B = \begin{bmatrix}\frac{1}{J_{p}} & 0 \\0 & {- \frac{1}{J_{v}}} \\\frac{\text{?}}{J_{p}i} & \frac{\text{?}}{J_{v}}\end{bmatrix}},{C = \begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0\end{bmatrix}},{{u = \begin{bmatrix}\text{?} \\T_{v}\end{bmatrix}};}}$ ?indicates text missing or illegible when filed

{dot over (θ)}_(B) is a rotation angle of an electric motor B; {dot over(θ)}_(v) is a rotation angle of a vehicle wheel; θ_(B) is a rotationalspeed of the electric motor; θ_(v) is a rotational speed of the vehiclewheel; {dot over (θ)}_(B) and θ_(v) are obtained by conductingintegration on the rotational speeds θ_(B) and θ_(v); T_(s) is a torqueof a drive shaft; C_(t) is a damping of a speed reducer; J_(P) is aninertia of a rotor of the electric motor B; i_(r) is a main speedreducer transmission ratio; C_(v) is a damping of the vehicle wheel;J_(v) is the sum of an inertia of the vehicle wheel and an equivalentinertia equivalent from a vehicle body to the vehicle wheel; k_(s) is arigidity of the drive shaft; C_(s) is a damping of the drive shaft; i isa transmission ratio of a main speed reducer; T_(P) is a torque of anoutput shaft of the driving system; T_(v) is a moment of resistance of avehicle;

an observability matrix of the driving system is

${N = \begin{bmatrix}C \\{CA} \\{CA}^{2}\end{bmatrix}};$

when a rank of the observability matrix N is 3, the driving system isobservable;

step 2: dividing the state of the driving system into blocks, andreconstructing state components of the driving system to obtain arewritten state observation equation of the driving system;

step 3: introducing transformation into the rewritten state equation ofthe driving system to obtain an expression equation and an errorequation of the Luenberger observer.

Further, step 2 specifically comprises:

the two measurable state variables are the output of the driving system:y=x₁=[θ_(B) θ_(v)]^(T); the state variable T_(s) needs to be observedand is recorded as x₂=[T_(s)]; because the rank of a matrix C is 2, thestate-space equation of the driving system is rewritten to be:

$\mspace{20mu} \left\{ {{{\begin{matrix}{\begin{bmatrix}{\overset{.}{x}}_{1} \\{\overset{.}{x}}_{2}\end{bmatrix} = {{\begin{bmatrix}A_{11} & A_{12} \\A_{21} & A_{22}\end{bmatrix}\begin{bmatrix}x_{1} \\x_{2}\end{bmatrix}} + {\begin{bmatrix}B_{1} \\B_{2}\end{bmatrix}u}}} \\{y = {{\begin{bmatrix}I & 0\end{bmatrix}\begin{bmatrix}x_{1} \\x_{2}\end{bmatrix}} = x_{1}}}\end{matrix}\mspace{20mu} {wherein}\mspace{14mu} A_{11}} = \begin{bmatrix}{- \frac{C_{i}}{J_{p}}} & 0 \\0 & {- \frac{C_{v}}{J_{v}}}\end{bmatrix}},{A_{12} = \begin{bmatrix}{- \frac{1}{J_{p}i}} \\\frac{1}{J_{v}}\end{bmatrix}},\mspace{20mu} {A_{21} = \begin{bmatrix}{\frac{i}{k_{s}} - \frac{\text{?}}{J_{p}i}} & {\frac{C_{s}C_{v}}{J_{v}} - k_{s}}\end{bmatrix}},{A_{22} = \left\lbrack {{- \frac{C_{s}}{J_{p}i^{2}}} - \frac{C_{s}}{J_{v}}} \right\rbrack},\mspace{20mu} {B_{1} = \begin{bmatrix}\frac{1}{J_{p}} & 0 \\0 & {- \frac{1}{J_{v}}}\end{bmatrix}},{{B_{2} = \begin{bmatrix}\frac{C_{s}}{J_{p}i} & \frac{C_{s}}{J_{v}}\end{bmatrix}};{\text{?}\text{indicates text missing or illegible when filed}}}} \right.$

I is a unit matrix;

the driving system is divided into two subsystems Λ₁ and Λ₂; the twosubsystems Λ₁ and Λ₂ are mutually coupled; a state equation of thesubsystem Λ₁ is:

$\quad\left\{ \begin{matrix}{{\overset{.}{x}}_{1} = {{A_{11}x_{1}} + {A_{12}x_{2}} + {B_{1}u}}} \\{y = x_{1}}\end{matrix} \right.$

a state equation of the subsystem Λ₂ is:

X ₂ =A ₂₁ x ₁ +A ₂₂ x ₂ +B ₂ u

the system state x₂=[T_(s)] of the subsystem Λ₂ is reconstructed; theinput and the output of the system state x₂ respectively are:

$\left\{ {\begin{matrix}{u_{oblu} = {{A_{21}x_{1}} + {B_{2}u}}} \\{y_{oblu} = {{\overset{.}{x}}_{1} - {A_{11}x_{1}} - {B_{1}u}}}\end{matrix};} \right.$

an output error feedback item G(y−ŷ) is introduced into the stateequation of the subsystem Λ₂ to obtain an observer equation of thedriving system as follows:

${\overset{.}{\hat{x}}}_{2} = {{{A_{21}x_{1}} + {A_{22}x_{2}} + {B_{2}u} + {G\left( {y - \hat{y}} \right)}} = {{\left( {A_{22} - {GA}_{12}} \right){\hat{x}}_{2}} + u_{oblu} + {Gy}_{oblu}}}$

wherein G is a feedback gain matrix; G=[g₁g₂]; g₁ is a feedback gain ofthe two measurable state variables; g₂ is a feedback gain of the statevariable T_(s).

Further, in step 3, transformation ŵ={circumflex over (x)}₁−Gy isintroduced into the rewritten observer equation of the driving system toobtain an expression equation and an error equation of the Luenbergerobserver as follows:

$\left\{ {{\begin{matrix}\begin{matrix}{\overset{.}{\hat{w}} = {{\left( {\frac{\text{?}}{i} - \frac{\text{?}}{J_{p}i} - \frac{\text{?}}{J_{p}}} \right)x_{1}} + {\left( {\frac{C_{s}C_{v}}{J_{v}} - k_{s} + \frac{C_{v}g_{2}}{J_{v}}} \right)x_{2}} +}} \\{{\left( {{- \frac{\text{?}}{J_{p}i^{2}}} - \frac{\text{?}}{J_{v}} + \frac{g_{1}}{J_{p}i} - \frac{g_{2}}{J_{v}}} \right){\hat{x}}_{3}} + {\left( {\frac{\text{?}}{J_{p}i} - \frac{g_{1}}{J_{p}}} \right)\text{?}} + {\left( {\frac{\text{?}}{J_{v}} + \frac{g_{2}}{J_{v}}} \right)T_{v}}}\end{matrix} \\{{\hat{x}}_{3} = {w + {g_{1}x_{1}} + {g_{2}x_{2}}}}\end{matrix}\mspace{20mu} {\overset{.}{\hat{x}}}_{3}} = {\left( {{- \frac{\text{?}}{J_{p}i^{2}}} - \text{?}} \right){\hat{x}}_{3}\text{?}\text{indicates text missing or illegible when filed}}} \right.$

The present invention has the following beneficial effects: the presentinvention feeds back the observer by utilizing the practical measurableinformation during vehicle running so as to reduce an error between anestimation result and an actual value. The present inventionreconstructs the state of the driving system such that the state of thedriving system has excellent observability. Additionally, the presentinvention introduces the transformation to reduce influence ofintegration on an observation result. Therefore, implementationdifficulty of the observer is reduced, an observation error is reduced,and application in practice is achieved.

BRIEF DESCRIPTION OF THE DRAWINGS

To describe the technical solutions in the embodiments of the presentinvention or the prior art more clearly, the following brieflyintroduces the accompanying drawings required for describing theembodiments or the prior art. Apparently, the accompanying drawings inthe following description show merely some embodiments in the presentinvention, and a person of ordinary skill in the art may still deriveother drawings from these accompanying drawings without creativeefforts.

FIG. 1 is a block diagram of a linear Luenberger observer.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The following clearly and completely describes the technical solutionsin the embodiments of the present invention with reference toaccompanying drawings in the embodiments of the present invention.Apparently, the described embodiments are merely a part rather than allof the embodiments of the present invention. All other embodimentsobtained by a person of ordinary skill in the art based on theembodiments of the present invention without creative efforts shall fallwithin the protection scope of the present invention.

A hybrid vehicle has three power sources, namely an engine, an electricmotor A and an electric motor B. The engine and the electric motor A arecoupled to drive front wheels of a vehicle. The electric motor B is usedfor driving rear wheels of the vehicle. Power batteries are electricallyconnected with the electric motor A and the electric motor B. Anexternal force acted on the vehicle during straight running mainlycomprises a traction force, a rolling resistance, an air resistance, agrade resistance, an acceleration resistance and the like. If suchexternal force is transformed into a moment of force acted on thevehicle, a kinetic equation of the driving system is shown as follows:

$\mspace{20mu} {\quad\left\{ {\begin{matrix}{{J_{P}{\overset{¨}{\theta}}_{B}} = {T_{P} - {C_{i}{\overset{.}{\theta}}_{B}} - {\frac{1}{\text{?}}T_{s}}}} \\{{J_{v}{\overset{¨}{\theta}}_{v}} = {T_{s} - {C_{v}{\overset{.}{\theta}}_{v}} - T_{v}}} \\{T_{s} = {{C_{s}\left( {\frac{{\overset{.}{\theta}}_{B}}{\text{?}} - {\overset{.}{\theta}}_{v}} \right)} + {k_{s}\left( {\frac{\theta_{B}}{i_{r}} - \theta_{v}} \right)}}}\end{matrix}\text{?}\text{indicates text missing or illegible when filed}} \right.}$

wherein {dot over (θ)}_(B) is a rotation angle of the electric motor B;{dot over (θ)}_(v) is a rotation angle of a vehicle wheel; θ_(B) is arotational speed of the electric motor; θ_(v) is a rotational speed ofthe vehicle wheel; {dot over (θ)}_(B) and {dot over (θ)}_(v) areobtained by conducting integration on the rotational speeds θ_(B) andθ_(v); J_(P) is an inertia of a rotor of the electric motor B; T_(P) isa torque of an output shaft of a driving system; C_(t) is a damping of aspeed reducer; i_(r) is a transmission ratio of a main speed reducer;J_(v) is the sum of an inertia of the vehicle wheel and an equivalentinertia equivalent from a vehicle body to the vehicle wheel; C_(v) is adamping of the vehicle wheel; C_(s) is a damping of the drive shaft;k_(s) is a rigidity of the drive shaft; T_(v) is a moment of resistanceof the vehicle; based on this, a state observer is built for the torqueT_(s) of the driving shaft to observe, wherein {umlaut over (θ)}_(B) isa rotation angle acceleration of the electric motor B, and {umlaut over(θ)}_(v) is a rotation angle acceleration of the vehicle wheel.

A method for constructing linear luenberger observer for vehicle controlcomprises the following steps:

step 1: building a state-space equation of a driving system of a vehicleto judge observability of the driving system;

wherein a state equation of the driving system is built by utilizing{dot over (θ)}_(B), {dot over (θ)}_(v) and T_(s) as state variables,{dot over (θ)}_(B) and {dot over (θ)}_(v) as the output of the drivingsystem, and T_(P) and T_(v) as the input of the driving system; thestate-space equation of the driving system is shown in equation (1):

$\begin{matrix}{\mspace{79mu} \left\{ {{{\begin{matrix}{\hat{x} = {{Ax} + {Bu}}} \\{y = {Cx}}\end{matrix}\mspace{20mu} {wherein}\mspace{14mu} x} = \begin{bmatrix}\text{?} \\\text{?} \\\text{?}\end{bmatrix}},\mspace{20mu} {A = \begin{bmatrix}{- \frac{\text{?}}{J_{P}}} & 0 & {- \frac{1}{J_{p}i_{v}}} \\0 & {- \frac{C_{v}}{J_{v}}} & \frac{1}{J_{v}} \\{\frac{\text{?}}{\text{?}} - \frac{\text{?}}{\text{?}}} & {\frac{C_{s}C_{v}}{J_{v}} - \text{?}} & {{- \frac{\text{?}}{J_{p}i_{r}^{2}}} - \frac{\text{?}}{J_{v}}}\end{bmatrix}},\mspace{20mu} {B = \begin{bmatrix}\frac{1}{J_{p}} & 0 \\0 & {- \frac{1}{J_{v}}} \\\frac{\text{?}}{J_{p}i} & \frac{\text{?}}{J_{v}}\end{bmatrix}},{C = \begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0\end{bmatrix}},{{{u = \begin{bmatrix}\text{?} \\T_{v}\end{bmatrix}};}\text{?}\text{indicates text missing or illegible when filed}}} \right.} & (1)\end{matrix}$

i is a transmission ratio of the main speed reducer, x is the input ofthe state-space equation, and y is the output of the state-spaceequation; therefore, an observability matrix of the driving system is

${N = \begin{bmatrix}C \\{CA} \\{CA}^{2}\end{bmatrix}};$

equation (1) is substituted into the observability matrix to obtain:

$\; {N = \begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\{- \frac{C_{i}}{J_{p}}} & 0 & {- \frac{1}{J_{p}i}} \\0 & {- \frac{C_{v}}{J_{v}}} & \frac{1}{J_{v}} \\\begin{matrix}{\frac{\text{?}}{J_{p}^{2}} -} \\{\frac{1}{J_{p}i}\left( {\frac{\text{?}}{i} - \frac{C_{s}C_{i}}{J_{p}i}} \right)}\end{matrix} & {{- \frac{1}{J_{p}i}}\left( {\frac{C_{s}C_{v}}{J_{v}} - \text{?}} \right)} & \begin{matrix}{\frac{C_{i}}{J_{p}^{2}i} +} \\{\frac{1}{J_{p}i}\left( {\frac{\text{?}}{J_{p}i^{2}} + \frac{C_{s}}{J_{v}}} \right)}\end{matrix} \\{\frac{1}{J_{v}}\left( {\frac{k_{s}}{i} - \frac{C_{s}C_{i}}{J_{p}i}} \right)} & {\frac{C_{v}^{2}}{J_{v}^{2}} + {\frac{1}{J_{v}}\left( {\frac{C_{s}C_{v}}{J_{v}} - k_{s}} \right)}} & \begin{matrix}{{- \frac{C_{v}}{J_{v}^{2}}} -} \\{\frac{1}{J_{v}}\left( {\frac{C_{s}}{J_{p}i^{2}} + \frac{\text{?}}{J_{v}}} \right)}\end{matrix}\end{bmatrix}}$ ?indicates text missing or illegible when filed

a rank (N) of the observability matrix of the driving system is 3, sothe driving system is observable;

step 2: dividing the state of the driving system into blocks accordingto the state-space equation of the driving system, and reconstructingstate components of the driving system to obtain a rewritten observerequation of the driving system;

the state variables {dot over (θ)}_(B) and {dot over (θ)}_(v) can bedirectly obtained through measurement, so, only a one-dimensiondimension-reduction observer needs to be built to reconstruct T_(s) tobuild a system with excellent dynamic property, strong robustness andoperation stability, thereby improving the observability of the system;

the two measurable state variables are the output of the driving system:y=x₁=[{dot over (θ)}_(B) {dot over (θ)}_(v)]^(T); the state variableT_(s) needs to be observed and is recorded as x₂=[T_(s)]; because therank (C) is 2, the state of the torque of the drive shaft of the drivingsystem is divided into the blocks, so the driving system can berewritten to be:

$\left\{ {{{\begin{matrix}{A = \begin{bmatrix}A_{11} & A_{12} \\A_{21} & A_{22}\end{bmatrix}} \\{{B = \begin{bmatrix}B_{1} \\B_{2}\end{bmatrix}}\mspace{70mu}} \\{{C = \left\lbrack {I\mspace{14mu} 0} \right\rbrack}\mspace{70mu}}\end{matrix}A_{11}} = \begin{bmatrix}{- \frac{C_{l}}{J_{p}}} & 0 \\0 & {- \frac{C_{v}}{J_{v}}}\end{bmatrix}},{A_{12} = \begin{bmatrix}{- \frac{1}{J_{P}i}} \\\frac{1}{J_{v}}\end{bmatrix}},{{{wherein}A_{21}} = \left\lbrack {\frac{k_{s}}{i} - {\frac{C_{s}C_{t}}{J_{P}i}\mspace{14mu} \frac{C_{s}C_{v}}{J_{v}}} - k_{s}} \right\rbrack},{A_{22} = \left\lbrack {{- \frac{C_{s}}{J_{P}i^{2}}} - \frac{C_{s}}{J_{v}}} \right\rbrack},{B_{1} = \begin{bmatrix}\frac{1}{J_{P}} & 0 \\0 & {- \frac{1}{J_{v}}}\end{bmatrix}},{{B_{2} = \left\lbrack {\frac{C_{s}}{J_{P}i^{2}}\mspace{14mu} \frac{C_{s}}{J_{v}}} \right\rbrack};}} \right.$

I is a unit matrix;

the rewritten state-space equation of the driving system is:

$\left\{ {\begin{matrix}{\begin{bmatrix}{\overset{.}{x}}_{1} \\{\overset{.}{x}}_{2}\end{bmatrix} = {{\begin{bmatrix}A_{11} & A_{12} \\A_{21} & A_{22}\end{bmatrix}\begin{bmatrix}x_{1} \\x_{2}\end{bmatrix}} + {\begin{bmatrix}B_{1} \\B_{2}\end{bmatrix}u}}} \\{{y = {{\left\lbrack {I\mspace{14mu} 0} \right\rbrack \begin{bmatrix}x_{1} \\x_{2}\end{bmatrix}} = x_{1}}}\mspace{160mu}}\end{matrix}\quad} \right.$

according to the state-space equation of the driving system, the drivingsystem is divided into two subsystems Λ₁ and Λ₂; the two subsystems Λ₁and Λ₂ are mutually coupled; a state equation of the subsystem Λ₁ is:

$\left\{ {\begin{matrix}{{\overset{.}{x}}_{1} = {{A_{11}x_{1}} + {A_{12}x_{2}} + {B_{1}u}}} \\{{y = x_{1}}\mspace{205mu}}\end{matrix}\quad} \right.$

a state equation of the subsystem Λ₂ is:

X ₂ =A ₂₁ x ₁ +A ₂₂ x ₂ +B ₂ u

the system state x₂=[T_(s)] of the subsystem Λ₂ is reconstructed; theinput and the output of the system state x₂ respectively are:

$\left\{ {\begin{matrix}{{u_{oblu} = {{A_{21}x_{1}} + {B_{2}u}}}\mspace{50mu}} \\{y_{oblu} = {{\overset{.}{x}}_{1} - {A_{11}x_{1}} - {B_{1}u}}}\end{matrix}\quad} \right.$

an output error feedback item G(y−ŷ) is introduced into the stateequation of the subsystem Λ₂, wherein G is a feedback gain matrix;G=[g₁g₂], g₁ is a feedback gain of two measurable state variables; g₂ isa feedback gain of the state variable T_(s); so the observer equation ofthe driving system is obtained:

$\begin{matrix}{{\overset{.}{\hat{x}}}_{2} = {{A_{21}x_{1}} + {A_{22}x_{2}} + {B_{2}u} + {G\left( {y - \hat{y}} \right)}}} \\{= {{\left( {A_{22} - {GA}_{12}} \right){\hat{x}}_{2}} + u_{oblu} + {Gy}_{oblu}}}\end{matrix}$

step 3: introducing transformation into the rewritten state equation ofthe driving system to correct the state equation of the driving system,thereby obtaining an equation and a structure of the linear Luenbergerobserver;

because the rewritten observer equation of the driving system has adifferential of an output quantity y of the driving system, theimplementation difficulty of state variable observation is increased.Additionally, high-frequency noise in an output signal of a rotationalspeed sensor is also amplified such that an observation error isincreased. To eliminate influence of the differential on the observationresult, transformation is introduced into the rewritten observerequation of the driving system ŵ={circumflex over (x)}₁−Gy;

the rewritten observer equation of the driving system is transformed tobe:

$\left\{ {\begin{matrix}{\overset{.}{\hat{w}} = {{\left( {A_{22} - {GA}_{12}} \right){\hat{x}}_{2}} + {\left( {A_{21} - {GA}_{11}} \right)y} + {\left( {B_{2} - {GB}_{1}} \right)u}}} \\{{{\hat{x}}_{2} = {\hat{w} + {Gy}}}\mspace{416mu}}\end{matrix}\quad} \right.$

observation of the torque T_(s) of the drive shaft is achieved by theobserver equation of the driving system in step 3;

a state estimation error equation of the driving system is:

{dot over ({tilde over (x)})}₂ =x ₂−{dot over ({circumflex over(x)})}₂=(A ₂₂ −GA ₁₂){tilde over (x)} ₂

a pole of (A₂₂−GA₁₂) is configured by utilizing a pole configurationmethod such that the estimation error {tilde over (x)}₂ is quicklyattenuated to be zero, thereby helping the estimation error {tilde over(x)}₂ to quickly attenuate to be zero; the state-space equation of thedriving system is substituted into the above equation to obtain anequation and a state observation error expression of the linearLuenberger observer to be:

$\left\{ {{{\begin{matrix}{{\overset{.}{\hat{w}} = {{\left( {\frac{k_{s}}{i} - \frac{C_{s}C_{l}}{J_{P}i} - \frac{C_{l}g_{1}}{J_{P}}} \right)x_{1}} + {\left( {\frac{C_{s}C_{v}}{J_{v}} - k_{s} + \frac{C_{v}g_{2}}{J_{v}}} \right)x_{2}} +}}\mspace{59mu}} \\{{\left( {{- \frac{C_{d}}{J_{P}i^{2}}} - \frac{C_{s}}{J_{v}} + \frac{g_{1}}{J_{P}i} - \frac{g_{2}}{J_{v}}} \right){\hat{x}}_{3}} + {\left( {\frac{C_{s}}{J_{P}i} - \frac{g_{1}}{J_{P}}} \right)T_{s}} + {\left( {\frac{C_{s}}{J_{v}} + \frac{g_{2}}{J_{v}}} \right)T_{v}}} \\{{{\hat{x}}_{3} = {\hat{w} + {g_{1}x_{1}} + {g_{2}x_{2}}}}\mspace{430mu}}\end{matrix}{\overset{.}{\overset{\sim}{x}}}_{3}} = {{\left( {{- \frac{C_{s}}{J_{P}i^{2}}} - \frac{C_{s}}{J_{v}} + \frac{g_{1}}{J_{P}i} - \frac{g_{2}}{J_{v}}} \right){\overset{\sim}{x}}_{3}{wherein}\mspace{14mu} x} = {\begin{bmatrix}x_{1} \\x_{2} \\x_{3}\end{bmatrix} = \begin{bmatrix}{\overset{.}{\theta}}_{B} \\{\overset{.}{\theta}}_{v} \\T_{s}\end{bmatrix}}}};} \right.$

the design of the linear Luenberger observer is completed. The structureof the linear Luenberger observer is shown in FIG. 1.

Each embodiment of the present specification is described in acorrelative manner, the same and similar parts between the embodimentsmay refer to each other, and each embodiment focuses on the differencefrom other embodiments. For a system disclosed in the embodiments, sinceit is basically similar to the method disclosed in the embodiments, thedescription is relatively simple, and reference can be made to themethod description.

The above merely describes preferred embodiments of the presentinvention, but are not used to limit the protection scope of the presentinvention. Any modifications, equivalent substitutions, improvements,and the like within the spirit and principles of the invention areintended to be included within the protection scope of the presentinvention.

1. A method for constructing linear Luenberger observer for vehiclecontrol, specifically comprising the following steps: step 1: building astate-space equation of a driving system of a vehicle to judgeobservability of the driving system; wherein a state equation of thedriving system is built by utilizing {dot over (θ)}_(B), {dot over(θ)}_(v) and T_(s) as state variables, {dot over (θ)}_(B) and {dot over(θ)}_(v) as the output of the driving system, and T_(P) and T_(v) as theinput of the driving system; the state-space equation of the drivingsystem is shown in equation (1): $\begin{matrix}\left\{ \begin{matrix}{\overset{.}{x} = {{Ax} + {Bu}}} \\{{y = {Cx}}\mspace{56mu}}\end{matrix} \right. & (1)\end{matrix}$ wherein x is the input of the state-space equation; y isthe output of the state-space equation; ${x = \begin{bmatrix}{\overset{.}{\theta}}_{B} \\{\overset{.}{\theta}}_{v} \\T_{s}\end{bmatrix}},{A = \begin{bmatrix}{- \frac{C_{l}}{J_{P}}} & 0 & {- \frac{1}{J_{P}i_{r}}} \\0 & {- \frac{C_{v}}{J_{v}}} & \frac{1}{J_{v}} \\{\frac{k_{s}}{i_{r}} - \frac{C_{s}C_{l}}{J_{P}i_{r}}} & {\frac{C_{s}C_{v}}{J_{v}} - k_{s}} & {{- \frac{C_{s}}{J_{P}i_{r}^{2}}} - \frac{C_{s}}{J_{v}}}\end{bmatrix}},{B = \begin{bmatrix}\frac{1}{J_{P}} & 0 \\0 & {- \frac{1}{J_{v}}} \\\frac{C_{s}}{J_{P}i} & \frac{C_{s}}{J_{v}}\end{bmatrix}},{C = \begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0\end{bmatrix}},{{u = \begin{bmatrix}T_{P} \\T_{v}\end{bmatrix}};}$ {dot over (θ)}_(B) is a rotation angle of an electricmotor B; {dot over (θ)}_(v) is a rotation angle of a vehicle wheel;θ_(B) is a rotational speed of the electric motor; θ_(v) is a rotationalspeed of the vehicle wheel; {dot over (θ)}_(B) and {dot over (θ)}_(v)are obtained by conducting integration on the rotational speeds θ_(B)and θ_(v); T_(s) is a torque of a drive shaft; C_(t) is a damping of aspeed reducer; J_(P) is an inertia of a rotor of the electric motor B;i_(r) is a main speed reducer transmission ratio; C_(v) is a damping ofthe vehicle wheel; J_(v) is the sum of an inertia of the vehicle wheeland an equivalent inertia equivalent from a vehicle body to the vehiclewheel; k_(s) is a rigidity of the drive shaft; C_(s) is a damping of thedrive shaft; i is a transmission ratio of a main speed reducer; T_(P) isa torque of an output shaft of the driving system; T_(v) is a moment ofresistance of a vehicle; an observability matrix of the driving systemis ${N = \begin{bmatrix}C \\{CA} \\{CA}^{2}\end{bmatrix}};$ when a rank of the observability matrix N is 3, thedriving system is observable; step 2: dividing the state of the drivingsystem into blocks, and reconstructing state components of the drivingsystem to obtain a rewritten state observation equation of the drivingsystem; step 3: introducing transformation into the rewritten stateequation of the driving system to obtain an expression equation and anerror equation of the Luenberger observer.
 2. The method forconstructing linear luenberger observer for vehicle control according toclaim 1, wherein step 2 specifically comprises the following steps: thetwo measurable state variables are the output of the driving system:y=x₁=[{dot over (θ)}_(B) {dot over (θ)}_(v)]^(T); the state variableT_(s) needs to be observed and is recorded as x₂=[T_(s)]; because therank of a matrix C is 2, the state-space equation of the driving systemis rewritten to be: $\left\{ {\begin{matrix}{\begin{bmatrix}{\overset{.}{x}}_{1} \\{\overset{.}{x}}_{2}\end{bmatrix} = {{\begin{bmatrix}A_{11} & A_{12} \\A_{21} & A_{22}\end{bmatrix}\begin{bmatrix}x_{1} \\x_{2}\end{bmatrix}} + {\begin{bmatrix}B_{1} \\B_{2}\end{bmatrix}u}}} \\{{y = {{\left\lbrack {I\mspace{14mu} 0} \right\rbrack \begin{bmatrix}x_{1} \\x_{2}\end{bmatrix}} = x_{1}}}\mspace{160mu}}\end{matrix}{\quad {{A_{11} = \begin{bmatrix}{- \frac{C_{l}}{J_{p}}} & 0 \\0 & {- \frac{C_{v}}{J_{v}}}\end{bmatrix}},{A_{12} = \begin{bmatrix}{- \frac{1}{J_{P}i}} \\\frac{1}{J_{v}}\end{bmatrix}},{{{wherein}A_{21}} = \left\lbrack {\frac{k_{s}}{i} - {\frac{C_{s}C_{t}}{J_{P}i}\mspace{14mu} \frac{C_{s}C_{v}}{J_{v}}} - k_{s}} \right\rbrack},{A_{22} = \left\lbrack {{- \frac{C_{s}}{J_{P}i^{2}}} - \frac{C_{s}}{J_{v}}} \right\rbrack},{B_{1} = \begin{bmatrix}\frac{1}{J_{P}} & 0 \\0 & {- \frac{1}{J_{v}}}\end{bmatrix}},{{B_{2} = \left\lbrack {\frac{C_{s}}{J_{P}i}\mspace{14mu} \frac{C_{s}}{J_{v}}} \right\rbrack};}}}} \right.$I is a unit matrix; the driving system is divided into two subsystems Λ₁and Λ₂; the two subsystems Λ₁ and Λ₂ are mutually coupled; a stateequation of the subsystem Λ₁ is: $\left\{ {\begin{matrix}{{\overset{.}{x}}_{1} = {{A_{11}x_{1}} + {A_{12}x_{2}} + {B_{1}u}}} \\{{y = x_{1}}\mspace{205mu}}\end{matrix}\quad} \right.$ a state equation of the subsystem Λ₂ is:X ₂ =A ₂₁ x ₁ +A ₂₂ x ₂ +B ₂ u the system state x₂=[T_(s)] of thesubsystem Λ₂ is reconstructed; the input and the output of the systemstate x₂ respectively are: $\left\{ {\begin{matrix}{{u_{oblu} = {{A_{21}x_{1}} + {B_{2}u}}}\mspace{50mu}} \\{y_{oblu} = {{\overset{.}{x}}_{1} - {A_{11}x_{1}} - {B_{1}u}}}\end{matrix}{\quad;}} \right.$ an output error feedback item G(y−ŷ) isintroduced into the state equation of the subsystem Λ₂ to obtain anobserver equation of the driving system as follows: $\begin{matrix}{{\overset{.}{\hat{x}}}_{2} = {{A_{21}x_{1}} + {A_{22}x_{2}} + {B_{2}u} + {G\left( {y - \hat{y}} \right)}}} \\{= {{\left( {A_{22} - {GA}_{12}} \right){\hat{x}}_{2}} + u_{oblu} + {Gy}_{oblu}}}\end{matrix}$ wherein G is a feedback gain matrix; G=[g₁g₂]; g₁ is afeedback gain of the two measurable state variables; g₂ is a feedbackgain of the state variable T_(s).
 3. The method for constructing linearluenberger observer for vehicle control according to claim 1, wherein instep 3, transformation ŵ={circumflex over (x)}₁−Gy is introduced intothe rewritten observer equation of the driving system to obtain anexpression equation and an error equation of the Luenberger observer asfollows: $\left\{ {{\begin{matrix}{{\overset{.}{\hat{w}} = {{\left( {\frac{k_{s}}{i} - \frac{C_{s}C_{l}}{J_{P}i} - \frac{C_{l}g_{1}}{J_{P}}} \right)x_{1}} + {\left( {\frac{C_{s}C_{v}}{J_{v}} - k_{s} + \frac{C_{v}g_{2}}{J_{v}}} \right)x_{2}} +}}\mspace{59mu}} \\{{\left( {{- \frac{C_{d}}{J_{P}i^{2}}} - \frac{C_{s}}{J_{v}} + \frac{g_{1}}{J_{P}i} - \frac{g_{2}}{J_{v}}} \right){\hat{x}}_{3}} + {\left( {\frac{C_{s}}{J_{P}i} - \frac{g_{1}}{J_{P}}} \right)T_{s}} + {\left( {\frac{C_{s}}{J_{v}} + \frac{g_{2}}{J_{v}}} \right)T_{v}}} \\{{{\hat{x}}_{3} = {\hat{w} + {g_{1}x_{1}} + {g_{2}x_{2}}}}\mspace{430mu}}\end{matrix}{\overset{.}{\overset{\sim}{x}}}_{3}} = {\left( {{- \frac{C_{s}}{J_{P}i^{2}}} - \frac{C_{s}}{J_{v}} + \frac{g_{1}}{J_{P}i} - \frac{g_{2}}{J_{v}}} \right){{\overset{\sim}{x}}_{3}.}}} \right.$